1. Field of the Invention
The present invention relates to Maximum Transition Run (MTR) codes and, more particularly, to Punctured MTR (PMTR) codes with an increased coding gain and an improved bit error rate, and an apparatus and method for providing the PMTR codes.
2. Description of Prior Art
In magnetic recording and reproducing systems, the process of encoding user input data to generate codewords to be stored on a recording medium is known as modulation encoding. In modulation encoding, user input data is converted to a codeword using a one-to-one mapping scheme. Generally, these codewords have additional bits compared to the bit size of the user input data. Modulation encoding helps to minimize errors from arising in the system due to noise in the communication channel.
Run-Length Limited (RLL) codes are one type of codes provided by using the modulation encoding technique. RLL codes, generally used in hard disc drives, have a code rate of "n/m" where "n" is an integer multiple or submultiple of 8 and "m" is an integer greater than "n". Generally, n-bit user data is input to an encoder and encoded into an m-bit codeword or channel data by the modulation encoding technique.
RLL codes have run length constraints that are represented using a condition (d, k), where "d" represents the minimum length of running 0's (or 1's) and "k" represents the maximum length of running 0's (or 1's). For example, a RLL code (0, 6) means that the code must have the minimum length of zero 0's and the maximum number of six 0's. Generally, RLL codes having a bit rate of 8/9, 16/17 and 24/25 are used in magnetic recording systems. In a 16/17 rate RLL code, 16-bit user data is input to an encoder and 17-bit codeword is output as channel data with a high efficiency of 0.94 (=16/17) or a rate loss of about 6%. However, such a RLL code results in minimum distance error-events. Minimum distance error events are described below in more detail.
In providing channel data to be recorded on a recording medium, e.g., magnetic disc, user input data is encoded into codewords and the codewords are recorded on the recording medium. Using a reproduction device, the recorded codewords are reproduced from the recording medium and decoded to generate original user data. An error event occurs when the recorded codewords having predetermined code sequences differ from the detected codewords. In order to improve system performance in magnetic recording using disc drive systems, certain code sequences which can result in such error events need to be eliminated.
Minimum distance error-events are known as most likely error-events having high probability of occurrence or as dominant error-events. The term, "minimum distance error-event" is used interchangeably with the term, "dominant error-event". It is desirable to increase the distance of minimum distance error-events to decrease the likelihood of such error-events. Although RLL codes offer a low rate loss, RLL codes are more prone to dominant error-events. Codes with dominant error-events (i.e., lacking distance enhancing properties) have no or low coding gain. Therefore, a group of codes that have distance enhancing properties, i.e., removing certain sequences from the code table that can result in minimum distance error-events, are needed.
Maximum transition run (MTR) codes have been proposed as a class of modulation codes designed to provide such distance enhancing properties. The MTR codes have been suggested to provide a coding gain necessary for high density magnetic recording. Generally, a standard MTR code provides a coding gain, i.e., avoids minimum distance error-events, at high densities by imposing a constraint that the codes to be recorded on a medium must not have more than two consecutive transitions or some other effective means of achieving the same goal. An example of such a standard MTR code is discussed below.
Symbols "1" and "-1" as shown in FIG. 1A represent two levels of a logic signal to be recorded on a recording medium. For example, a code sequence of "1 -1" or "1 1" has one transition therein, and a code sequence of "1 -1" has two consecutive transitions where the first transition occurs from "1" to "-1" and the second transition from "-1" to "1". In high density recording, one of the dominant error-events is mistaking -1 1 -1 recorded on a recording medium as 1 -1 1 when the recorded data is detected, or mistaking 1 -1 1 recorded on the medium as -1 1 -1. A set of MTR constraints to eliminate such dominant error-events from all possible code sequences is discussed in an article entitled "Time-varying MTR Codes for High Density Magnetic Recording", ICC 97, November 1997. In the article, four possible cases of dominant error-events as shown in FIG. 1A are discussed.
In FIG. 1A, five bit slots are shown; however, these code sequences can be found in a larger bit-size code. The cases I-IV represent possible codeword sequences which could result in the dominant error-events. All possible levels for the bits preceding and following the code sequence "1 -1 1" or "-1 1 -1" in the first and fifth bit slots are covered by the four cases.
As shown in FIG. 1A, each of the cases I-IV has a pair of code sequences. When one of the two sequences in each of the cases I-IV is recorded and the other sequence is detected, a dominant error-event occurs. Therefore, at least one of the two sequences in the cases I-IV needs to be eliminated from the code table to avoid occurrence of dominant error-events. By imposing a constraint that no three consecutive transitions are allowed in a code sequence, at least one of the two sequences in each of the cases I-IV is eliminated. This type of standard MTR code provides a coding gain.
For higher capacity recording, another type of MTR constraint, known as a time-varying MTR constraint, is proposed in the article. In the time-varying MTR codes, at most three consecutive transitions are allowed such that the cases I and II are eliminated. In the cases III and IV, it is observed that three consecutive transitions end at even or odd bit slots, as shown in FIG. 1B. By imposing a constraint that no four consecutive transitions are allowed and that no three consecutive transitions ending in even bit slots are allowed, dominant error-events for high density recording can be eliminated and MTR codes with distance enhancing properties are provided.
FIG. 2 illustrates an example of a 8/9 rate MTR code with such a constraint condition. "A" represents a transition allowed in the bit slot marked with "A. As shown in FIG. 2, this 8/9 MTR code eliminates minimum distance error-events by:
1) allowing at most two transitions in the first and second bit slots of the 9-bit codeword taking into consideration the previous codeword, PA1 2) allowing at most one transition in the last bit slot of the 9-bit codeword, and PA1 3) allowing a third transition only in the bit slots marked with "A" in the 9-bit codeword.
All other code sequences for the 8/9 MTR code are eliminated to avoid dominant error-events. Using a computer simulation, the above constraints provide 267 possible codewords. Eleven more codewords can be removed for run-length constraint reasons which still results in 256 valid codewords needed to achieve a 8/9 code rate.
However, these MTR codes have a much lower data rate than RLL codes. For example, RLL coding provides a 16/17 rate code but MTR coding provides a 8/9 rate code with an additional 6% rate loss over the 16/17 RLL code. Due to the 6% rate loss, the channel data rate for the MTR codes has to be at least 6% greater than that for the RLL codes to compensate for the rate loss. This results in an increased noise bandwidth and a greater equalization loss. That is, any increase in the coding gain achieved by using the above-described MTR code is partially or fully offset by the rate loss of the MTR code. Accordingly, a channel code which provides sufficient coding gain with a minimum rate loss is needed, especially for high order partial response channels.